Simplify 3 square root of 45-8 square root of 20

$3 \sqrt{45} - 8 \sqrt{20}$

Step 1

Simplify each term.

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$3 \sqrt{9 (5)} - 8 \sqrt{20}$

Rewrite $9$ as $3^{2}$ .

$3 \sqrt{3^{2} \cdot 5} - 8 \sqrt{20}$

$3 \sqrt{3^{2} \cdot 5} - 8 \sqrt{20}$

Pull terms out from under the radical.

$3 (3 \sqrt{5}) - 8 \sqrt{20}$

Multiply $3$ by $3$ .

$9 \sqrt{5} - 8 \sqrt{20}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$9 \sqrt{5} - 8 \sqrt{4 (5)}$

Rewrite $4$ as $2^{2}$ .

$9 \sqrt{5} - 8 \sqrt{2^{2} \cdot 5}$

$9 \sqrt{5} - 8 \sqrt{2^{2} \cdot 5}$

Pull terms out from under the radical.

$9 \sqrt{5} - 8 (2 \sqrt{5})$

Multiply $2$ by $- 8$ .

$9 \sqrt{5} - 16 \sqrt{5}$

$9 \sqrt{5} - 16 \sqrt{5}$

Step 2

Subtract $16 \sqrt{5}$ from $9 \sqrt{5}$ .

$- 7 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 7 \sqrt{5}$

Decimal Form:

$- 15.65247584 \dots$

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